Consistent aggregation with superlative and other price indices

Various fields of economic analysis (e.g. growth and productivity) and economic policy (e.g. monetary and social policy) rely on accurate measures of price change. Unfortunately, the price index formulae that most price statisticians consider as particularly accurate—the superlative indices of Fisher, Törnqvist, and Walsh—are believed to violate the property of consistency in aggregation. This property, however, is indispensable for economic studies that attempt to disaggregate the overall result into the contributions of individual entities such as sectors of the economy or groups of products. The present paper introduces a thoroughly motivated formal definition of consistency in aggregation and proves that, contrary to general perception, the three superlative price indices can be considered as consistent in aggregation. Furthermore, many other price indices are shown to be consistent in aggregation. The theoretical findings are applied to the Swedish consumer price index.